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<LI><B>Paperback:</B> 602 pages <br>
<LI><B>Publisher:</B> Springer Verlag, New York; 2nd ed. 2001. 2nd printing edition (June 1, 2007) <br>
<LI><B>Language:</B> English </LI>
<LI><STRONG>Review<br></STRONG>
<P>From the reviews of the second edition:</P>
<P>SHORT BOOK REVIEWS</P>
<P>"The text reads fluently and beautifully throughout, with light, good-humoured touches that warm the reader without being intrusive. There are many examples and exercises, some of which draw out the essence of work of other authors. Each chapter ends with a "Notes" section containing further brief descriptions of research papers. A reference section lists about eight hundred and sixty references. Each chapter begins with a quotation from "The Wheel of Time" a sequence of books by Robert Jordan. Only a few displays and equations have numbers attached. This is an extremely fine, exceptional text of the highest quality."<br>ISI Short Book Reviews, April 2002</P>
<P>JOURNAL OF MATHEMATICAL PSYCHOLOGY</P>
<P>"This book is an excellent introduction to Bayesian statistics and decision making. The author does an outstanding job in explicating the Bayesian research program and in discussing how Bayesian statistics differs form fiducial inference and from the Newman-Pearson likelihood approach…The book would be well suited for a graduate-level course in a mathematical statistics department. There are numerous examples and exercises to enhance a deeper understanding of the material. The writing is authoritative, comprehensive, and scholarly."</P>
<P>"This book is a publication in the well-known Springer Series in statistics published in 2001. It is a textbook that presents an introduction to Bayesian statistics and decision theory for graduate level course … . The textbook contains a wealth of references to the literature; therefore it can also be recommended as an important reference book for statistical researchers. … for those who want to make a Bayesian choice, I recommend that you make your choice by getting hold of Robert’s book, The Bayesian Choice." (Jan du Plessis, Newsletter of the South African Statistical Association, June, 2003)</P>
<P>"This is the second edition of the author’s graduate level textbook ‘The Bayesian choice: a decision-theoretic motivation.’ … The present book is a revised edition. It includes important advances that have taken place since then. Different from the previous edition is the decreased emphasis on decision-theoretic principles. Nevertheless, the connection between Bayesian Statistics and Decision Theory is developed. Moreover, the author emphasizes the increasing importance of computational techniques." (Krzysztof Piasecki, Zentralblatt MATH, Vol. 980, 2002)</P></LI>
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<P><STRONG>Book Description<br></STRONG></P>
<P><STRONG>Winner of the 2004 DeGroot Prize</STRONG></P>
<P>The DeGroot Prize is awarded every two years by the International Society</P>
<P>for Bayesian Analysis in recognition of an important, timely, thorough and</P>
<P>notably original contribution to the statistics literature.</P>
<P>This graduate-level textbook presents an introduction to Bayesian statistics and decision theory. Its scope covers both the basic ideas of statistical theory, and also some of the more modern and advanced topics of Bayesian statistics such as complete class theorems, the Stein effect, Bayesian model choice, hierarchical and empirical Bayes modeling, Monte Carlo integration, including Gibbs sampling and other MCMC techniques. <br>The second edition includes a new chapter on model choice (Chapter 7) and the chapter on Bayesian calculations (6) has been extensively revised. Chapter 4 includes a new section on dynamic models. In Chapter 3, the material on noninformative priors has been expanded, and Chapter 10 has been supplemented with more examples. The Bayesian Choice will be suitable as a text for courses on Bayesian analysis, decision theory or a combination of them. </P></LI>
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<P><STRONG><FONT size=5>Contents</FONT></STRONG><br>Preface to the Paperback Edition vii<br>Preface to the Second Edition ix<br>Preface to the First Edition xiii<br>List of Tables xxiii<br>List of Figures xxv<br><STRONG>1 Introduction 1</STRONG><br>1.1 Statistical problems and statistical models 1<br>1.2 The Bayesian paradigm as a duality principle 8<br>1.3 Likelihood Principle and Sufficiency Principle 13<br>1.4 Prior and posterior distributions 22<br>1.5 Improper prior distributions 26<br>1.6 The Bayesian choice 31<br>1.7 Exercises 31<br>1.8 Notes 45<br><STRONG>2 Decision-Theoretic Foundations 51<br></STRONG>2.1 Evaluating estimators 51<br>2.2 Existence of a utility function 54<br>2.3 Utility and loss 60<br>2.4 Two optimalities: minimaxity and admissibility 65<br>2.5 Usual loss functions 77<br>2.6 Criticisms and alternatives 83<br>2.7 Exercises 85<br>2.8 Notes 96<br><STRONG>3 From Prior Information to Prior Distributions 105</STRONG><br>3.1 The difficulty in selecting a prior distribution 105<br>3.2 Subjective determination and approximations 106<br>3.3 Conjugate priors 113<br>3.4 Criticisms and extensions 123<br>3.5 Noninformative prior distributions 127<br>3.6 Posterior validation and robustness 141<br>3.7 Exercises 144<br>3.8 Notes 158<br><STRONG>4 Bayesian Point Estimation 165</STRONG><br>4.1 Bayesian inference 165<br>4.2 Bayesian Decision Theory 173<br>4.3 Sampling models 180<br>4.4 The particular case of the normal model 186<br>4.5 Dynamic models 193<br>4.6 Exercises 201<br>4.7 Notes 216<br><STRONG>5 Tests and Confidence Regions 223</STRONG><br>5.1 Introduction 223<br>5.2 A first approach to testing theory 224<br>5.3 Comparisons with the classical approach 242<br>5.4 A second decision-theoretic approach 256<br>5.5 Confidence regions 259<br>5.6 Exercises 267<br>5.7 Notes 279<br><STRONG>6 Bayesian Calculations 285</STRONG><br>6.1 Implementation difficulties 285<br>6.2 Classical approximation methods 293<br>6.3 Markov chain Monte Carlo methods 301<br>6.4 An application to mixture estimation 318<br>6.5 Exercises 321<br>6.6 Notes 334<br><STRONG>7 Model Choice 343</STRONG><br>7.1 Introduction 343<br>7.2 Standard framework 348<br>7.3 Monte Carlo and MCMC approximations 356<br>7.4 Model averaging 366<br>7.5 Model projections 369<br>7.6 Goodness-of-fit 374<br>7.7 Exercises 377<br>7.8 Notes 386<br><STRONG>8 Admissibility and Complete Classes 391</STRONG><br>8.1 Introduction 391<br>8.2 Admissibility of Bayes estimators 391<br>8.3 Necessary and sufficient admissibility conditions 400<br>8.4 Complete classes 409<br>8.5 Necessary admissibility conditions 412<br>8.6 Exercises 416<br>8.7 Notes 425<br><STRONG>9 Invariance, Haar Measures, and Equivariant Estimators 427</STRONG><br>9.1 Invariance principles 427<br>9.2 The particular case of location parameters 429<br>9.3 Invariant decision problems 431<br>9.4 Best equivariant noninformative distributions 436<br>9.5 The Hunt–Stein theorem 441<br>9.6 The role of invariance in Bayesian Statistics 445<br>9.7 Exercises 446<br>9.8 Notes 454<br><STRONG>10 Hierarchical and Empirical Bayes Extensions 457</STRONG><br>10.1 Incompletely Specified Priors 457<br>10.2 Hierarchical Bayes analysis 460<br>10.3 Optimality of hierarchical Bayes estimators 474<br>10.4 The empirical Bayes alternative 478<br>10.5 Empirical Bayes justifications of the Stein effect 484<br>10.6 Exercises 490<br>10.7 Notes 502<br><STRONG>11 A Defense of the Bayesian Choice 507</STRONG><br><STRONG>A Probability Distributions 519<br>B Usual Pseudo-random Generators 523<br>C Notations 527<br>References 531<br>Author Index 579<br>Subject Index 587</STRONG></P></LI>
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